Theodosius <Bithynius>; Clavius, Christoph - Theodosii Tripolitae Sphaericorum libri tres

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9482

THEOREMA 9. PROPOS. 9.

118.

SI polus parallelorum ſit in circunſerentia ma-
ximi circuli, quem duo alij maximi circuli ad an -
gulos rectos ſecent, quorum circulorum alter ſit
vnus parallelorũ, alter verò ad parallelos obliquus
ſit: & ab hoc obliquo circulo ſumantur æquales
circunferentiæ, quæ continuæ quidem non ſint,
ſed tamen ſint ad eaſdem partes maximi illius pa-
ralleli; per polum autem, & ſingula puncta æqua-
les circunferentias terminantia deſcribantur ma-
ximi circuli: Inæquales circunferentias de maxi-
mo parallelo intercipient, quarum ea, quæ pro-
pior erit maximo circulo primo poſito, ſemper
erit maior remotiore.

IN circunſerentia maximi circuli A B, ſit A, polus parallelorum, eum-
que ſecent duo maximi circuli B C, D C, ad angulos rectos, quorum B C,
ſit maximus parallelorum, & D C, ad parallelos obliquus; ex quo ſuman-
tur arcus æquales non continui E F, G H: & per puncta E, F, G, H, & polum
A, deſcribantur maximi circuli A E I, A F K, A G L, A H M. Dico arcum M L,
2220. 1. huius maiorem eſſe arcu K I. Autenim intermedius arcus F G, vtrique æqualium

100[Figure 100] E F, G H, commenſurabilis eſt, aut incommen
ſurabilis. Sit primum commenſurabilis. In-
uenta autem maxima communi menſura X,
334. decimi. diuidantur tres arcus E F, F G, G H, in par-
tes ipſi X, æquales, vt in prima figura appa-
ret; & per puncta diuiſionum, & polum A,
circuli maximi ducantur. Quoniam igitur ar-
4420. 1. huius. cus E Q, Q F, F P, & c. æquales ſunt, ma-
ior erit arcus M R, arcu R L, & R L, maior,
556. huius. quàm L, S, & c. Igitur cum M R, maior ſit
quàm K V, & R L, maior quàm V I, erit &
totus M L, maior toto K I. quod eſt propo-
ſitum.

SED iam ſit arcus intermedius F G, in
commenſurabilis vtrique arcuum æqualium E F, G H. Dico Rurſus arcum
M L, maiorem eſſe arcu K I. Si enim maior non eſt, erit vel minor, vel æqua-
lis. Sit primum, ſi ſieri poteſt, M L, minor quàm K I, vt in ſecunda figura;

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Scan	Original
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Scan	Original
91	79
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95	83
96	84
97	85
98	86
99	87
100	88
101	89
102	90
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104	92
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107	95
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109
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